IVR: Open- and Closed-Loop Control. M. Herrmann

Transcription

1 IVR: Open- and Closed-Loop Control M. Herrmann

2 Overview Open-loop control Feed-forward control Towards feedback control

3 Controlling the motor over time Process model V B = k 1 s + M k 2 R ds dt Stationary behaviour (steady state) s (t ) = V B k 1 Inverse model: V B = k 1 s goal Solution provides forward model: s (t) = s 0 e MR (t t k 1 k 0 ) V ( ) B e MR (t t k 1 k 0 ) 2 k 1

4 The control problem Forward: Given the control signals, can we predict the motion of the robot? Inverse: Given the desired motion of the robot: Can we determine the right control signals? Control theory aims at unique or easy exact solutions Difficult in the presence of non-linearities or noise

5 Open loop control Examples: To execute a memorised trajectory, produce appropriate sequence of motor torques To obtain a goal, make a plan and execute it means-ends reasoning could be seen as inverting a forward model of cause-effect Ballistic movements such as saccades

6 Open loop control Potentially cheap and simple to implement e.g. if solution is already known. Fast, e.g. useful if feedback would come too late. Benefits from calibration e.g. tune parameters of approximate model. If model unknown, may be able to use statistical learning methods to find a good fit e.g. using neural networks

7 Open loop control Neglects possibility of disturbances, which might affect the outcome. Disturbances For example: Change in temperature may change the friction in all the robot joints. Unexpected obstacle may interrupt trajectory

8 Feed-forward control One solution is to measure the (potential) disturbance and use this to adjust the control signals. For example Thermometer signal alters friction parameter. Obstacle detection produces alternative trajectory.

9 Feed-forward control Can sometimes be effective and efficient. Requires anticipation, not just of the robot process characteristics, but of possible changes in the world. Does not provide or use knowledge of actual output (for this need to use feedback control).

10 Control paradigms Open loop control Feed-forward control Disturbances? Feedback control

11 Combining control methods In practise most robot systems require a combination of control methods Robot arm using servos on each joint to obtain angles required by geometric inverse model Forward model predicts feedback, so can use in fast control loop to avoid problems of delay Feed-forward: Measurements of disturbances can be used to adjust feedback control parameters Training of an open-loop system is essentially a feedback process

12 Feedback control Example: Watt governor

13 Compare: Room heating Open loop: For desired temperature, switch heater on, and after pre-set time, switch off. Feed forward: Use thermometer outside room to compensate timer for external temperature. Feedback: Use thermometer inside room to switch off when desired temperature reached. NO PREDICTION REQUIRED!

14 Control laws in feed-back control On-off: Switch system if desired = actual Servo: control signal proportional to difference between desired and actual, e.g. spring:

15 Complex control law May involve multiple inputs and outputs E.g. homeostatic control of human body temperature Multiple temperature sensors linked to hypothalamus in brain Depending on difference from desired temperature, regulates sweating, vasodilation, piloerection, shivering, metabolic rate, behaviour... Result is reliable core temperature control

16 Negative vs. Positive Feedback Examples so far have been negative feedback: control law involves subtracting the measured output, acting to decrease difference. Positive feedback results in amplification: e.g. microphone picking up its own output e.g. runaway selection in evolution Generally taken to be undesirable in robot control, but sometimes can be effective e.g. in exploratory control, self-excitation model of stick insect walking (H. Cruse et al., 1995) to counteract negative feedback from the environment

17 Stick insect walking 6-legged robot has 18 degrees of mobility. Difficult to derive co-ordinated control laws But have linked system: movement of one joint causes appropriate change to all other joints. Can use signal in a feed-forward loop to control 12 joints (remaining 6 use feedback to resist gravity).

18 Advantages of feedback control Major advantage is that (at least in theory) feedback control does not require a model of the process. E.g. thermostats work without any knowledge of the dynamics of room heating (except for time scales and gains) Thus controller can be very simple and direct E.g. hardware governor does not even need to do explicit measurement, representation and comparison Can (potentially) produce robust output in the face of unknown and unpredictable disturbances E.g. homeostatic body temperature control keeps working in unnatural environments

19 Issues to be solved Requires sensors capable of measuring output Not required by open-loop or feed-forward Low gain is slow, high gain is unstable Delays in feedback loop will produce oscillations (or worse) In practise, need to understand process to obtain good control: E.g. James Clerk Maxwell s analysis of dynamics of the Watt governor